X-ray reflectometry apparatus and method thereof for measuring three dimensional nanostructures on flat substrate
This disclosure relates to an X-ray reflectometry apparatus and a method for measuring a three-dimensional nanostructure on a flat substrate. The X-ray reflectometry apparatus comprises an X-ray source, an X-ray reflector, a 2-dimensional X-ray detector, and a two-axis moving device. The X-ray source is for emitting X-ray. The X-ray reflector is configured for reflecting the X-ray onto a sample surface. The 2-dimensional X-ray detector is configured to collect a reflecting X-ray signal from the sample surface. The two-axis moving device is configured to control two-axis directions of the 2-dimensional X-ray detector to move on at least one of x-axis and z-axis with a formula concerning an incident angle of the X-ray with respect to the sample surface for collecting the reflecting X-ray signal.
1. An X-ray reflectometry apparatus for measuring a three-dimensional nanostructure on a flat substrate, comprising:
an X-ray source for emitting X-ray;
an X-ray reflector configured for reflecting the X-ray onto a sample surface;
a 2-dimensional X-ray detector configured to collect a reflecting X-ray signal from the sample surface; and
a two-axis moving device configured to control two-axis directions of the 2-dimensional X-ray detector to move on at least one of x-axis and z-axis with a formula concerning an incident angle of the X-ray with respect to the sample surface for collecting the reflecting X-ray signal.
2. The X-ray reflectometry apparatus according to claim 1 , wherein the two-axis moving device comprises an x-axis moving device and a z-axis moving device, wherein the x-axis moving device is configured to control the 2-dimensional X-ray detector to move on the x-axis, the z-axis moving device is configured to control the 2-dimensional X-ray detector to move on the z-axis.
3. The X-ray reflectometry apparatus according to claim 1 , further comprising a rotating device configured for rotating the 2-dimensional X-ray detector in x-z plane.
4. The X-ray reflectometry apparatus according to claim 1 , wherein when the incident angle of the X-ray with respect to the sample surface is set as a range from θ′ to θ′+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula:
W
<
L
tan
(
θ
′
+
Δθ
)
-
tan
θ
′
,
wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, L is a size of the 2-dimensional X-ray detector along the z-axis.
5. The X-ray reflectometry apparatus according to claim 1 , wherein when the incident angle of the X-ray with respect to the sample surface is set as a range from θ′ to θ′+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the z-axis with a formula: H=W·tan θ′+L/2, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis, L is a size of the 2-dimensional X-ray detector along the z-axis.
6. The X-ray reflectometry apparatus according to claim 1 , wherein when the incident angle of the X-ray with respect to the sample surface is set as a range from θ′ to θ′+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula of
W
<
L
tan
(
θ
′
+
Δθ
)
-
tan
θ
′
,
and at the same time move on the z-axis with a formula of H=W·tan θ′+L/2, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, L is a size of the 2-dimensional X-ray detector along the z-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis.
7. The X-ray reflectometry apparatus according to claim 1 , wherein when the incident angle of the X-ray with respect to the sample surface is θ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the z-axis with a formula: H=W·tan θ, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis.
8. The X-ray reflectometry apparatus according to claim 7 , wherein a moving deviation of the 2-dimensional X-ray detector on the z-axis is within ±L/2, wherein L is a size of the 2-dimensional X-ray detector along the z-axis.
9. The X-ray reflectometry apparatus according to claim 7 , wherein when the incident angle of the X-ray with respect to the sample surface is changed from θ to θ+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move with a distance ΔH on the z-axis with a formula: ΔH=W·tan(θ+Δθ)−W·tan θ.
10. The X-ray reflectometry apparatus according to claim 9 , wherein a moving deviation of the 2-dimensional X-ray detector on the z-axis is within ±L/2, wherein L is a size of the 2-dimensional X-ray detector along the z-axis.
11. The X-ray reflectometry apparatus according to claim 1 , wherein when the incident angle of the X-ray with respect to the sample surface is set to be θ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula: W=H·cot θ, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis.
12. The X-ray reflectometry apparatus according to claim 11 , wherein when the incident angle of the X-ray with respect to the sample surface is changed from θ to θ+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula: W=H·cot (θ+Δθ).
13. The X-ray reflectometry apparatus according to claim 1 , wherein when the incident angle of the X-ray with respect to the sample surface is set to be θ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis within a distance range from
(
H
-
L
2
)
·
cot
θ
to
(
H
+
L
2
)
·
cot
θ
,
wherein L is a size of the 2-dimensional X-ray detector along the z-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis,
(
H
+
L
2
)
·
cot
θ
is a maximum distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector,
(
H
-
L
2
)
·
cot
θ
is a minimum distance between the X ray-reflection point on the sample surface and the surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector.
14. The X-ray reflectometry apparatus according to claim 13 , wherein when the incident angle of the X-ray with respect to the sample surface is changed from θ to θ+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis within a distance range from
(
H
-
L
2
)
·
cot
(
θ
+
Δθ
)
to
(
H
+
L
2
)
·
cot
(
θ
+
Δθ
)
,
wherein
(
H
+
L
2
)
·
cot
(
θ
+
Δθ
)
is a maximum distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector,
(
H
-
L
2
)
·
cot
(
θ
+
Δθ
)
is a minimum distance between the X ray-reflection point on the sample surface and the surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector.
15. A method for measuring a three-dimensional nanostructure on a flat substrate comprising:
emitting X-ray by an X-ray source;
reflecting the X-ray onto a sample surface by an X-ray reflector;
collecting a reflecting X-ray signal from the sample surface by a 2-dimensional X-ray detector; and
controlling two-axis directions of the 2-dimensional X-ray detector by a two-axis moving device to move on at least one of x-axis and z-axis with a formula concerning an incident angle of the X-ray with respect to the sample surface for collecting the reflecting X-ray signal.
16. The method according to claim 15 , wherein the two-axis moving device comprises an x-axis moving device and a z-axis moving device, wherein the x-axis moving device is configured to control the 2-dimensional X-ray detector to move on the x-axis, the z-axis moving device is configured to control the 2-dimensional X-ray detector to move on the z-axis.
17. The method according to claim 15 , further comprising rotating the 2-dimensional X-ray detector in x-z plane by a rotating device.
18. The method according to claim 15 , wherein when the incident angle of the X-ray with respect to the sample surface is set as a range from θ′ to θ′+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula:
W
<
L
tan
(
θ
′
+
Δθ
)
-
tan
θ
′
,
wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, L is a size of the 2-dimensional X-ray detector along the z-axis.
19. The method according to claim 15 , wherein when the incident angle of the X-ray with respect to the sample surface is set as a range from θ′ to θ′+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the z-axis with a formula: H=W·tan θ′+L/2, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis, L is a size of the 2-dimensional X-ray detector along the z-axis.
20. The method according to claim 15 , wherein when the incident angle of the X-ray with respect to the sample surface is set as a range from θ′ to θ′+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula of
W
<
L
tan
(
θ
′
+
Δθ
)
-
tan
θ
′
,
and at the same time move on the z-axis with a formula of H=W·tan θ′+L/2, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, L is a size of the 2-dimensional X-ray detector along the z-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis.
21. The method according to claim 15 , wherein when the incident angle of the X-ray with respect to the sample surface is θ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the z-axis with a formula: H=W·tan θ, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis.
22. The method according to claim 21 , wherein a moving deviation of the 2-dimensional X-ray detector on the z-axis is within ±L/2, wherein L is a size of the 2-dimensional X-ray detector along the z-axis.
23. The method according to claim 21 , wherein when the incident angle of the X-ray with respect to the sample surface is changed from θ to θ+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move with a distance ΔH on the z-axis with a formula: ΔH=W·tan(θ+Δθ)−W·tan θ.
24. The method according to claim 23 , wherein a moving deviation of the 2-dimensional X-ray detector on the z-axis is within ±L/2, wherein L is a size of the 2-dimensional X-ray detector along the z-axis.
25. The method according to claim 15 , wherein when the incident angle of the X-ray with respect to the sample surface is set to be θ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula: W=H·cot θ, wherein W is a distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis.
26. The method according to claim 25 , wherein when the incident angle of the X-ray with respect to the sample surface is changed from θ to θ+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis with a formula: W=H·cot (θ+Δθ).
27. The method according to claim 15 , wherein when the incident angle of the X-ray with respect to the sample surface is set to be θ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis within a distance range from
(
H
-
L
2
)
·
cot
θ
to
(
H
+
L
2
)
·
cot
θ
,
wherein L is a size of the 2-dimensional X-ray detector along the z-axis, H is a distance between the sample surface and a center of the 2-dimensional X-ray detector along the z-axis,
(
H
+
L
2
)
·
cot
θ
is a maximum distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector,
(
H
-
L
2
)
·
cot
θ
is a minimum distance between the X ray-reflection point on the sample surface and the surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector.
28. The method according to claim 27 , wherein when the incident angle of the X-ray with respect to the sample surface is changed from θ to θ+Δθ, the two-axis moving device controls the 2-dimensional X-ray detector to move on the x-axis within a distance range from
(
H
-
L
2
)
·
cot
(
θ
+
Δθ
)
to
(
H
+
L
2
)
·
cot
(
θ
+
Δθ
)
,
wherein
(
H
+
L
2
)
·
cot
(
θ
+
Δθ
)
is a maximum distance between a X ray-reflection point on the sample surface and a surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector,
(
H
-
L
2
)
·
cot
(
θ
+
Δθ
)
is a minimum distance between the X ray-reflection point on the sample surface and the surface of the 2-dimensional X-ray detector along the x-axis that the reflecting X-ray signal can arrive at the 2-dimensional X-ray detector.